Thermodynamic relations

These thermodynamic relations are also known as coefficient relations.

$T=\left(\frac{\partial U}{\partial S}\right)_V$

$p=-\left(\frac{\partial U}{\partial V}\right)_S$

$T=\left(\frac{\partial H}{\partial S}\right)_p$

$V=\left(\frac{\partial H}{\partial p}\right)_S$

$S=-\left(\frac{\partial A}{\partial T}\right)_V$

$p=-\left(\frac{\partial A}{\partial V}\right)_T$

$S=-\left(\frac{\partial G}{\partial T}\right)_p$

$V=\left(\frac{\partial G}{\partial p}\right)_T$

where

[edit] See also